Jimmy had a total of 163 apples and oranges. After selling 50% of all the apples and 20% of all the oranges, he had 110 fruits left. How many oranges did Jimmy have at first?
Let x = # of apples and y = # of oranges.
x + y = 163
x = 163 - y
.5x + .8y = 110
Substitute 163-y for x in last equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
let the number of apples be x
let the number of oranges be y
x+y = 163 ---> y = 163-x
.5x + .8y = 110
5x + 8y = 1100
use substitution
5x + 8(163-x) = 1100
5x + 1304 - 8x = 1100
-3x = -204
x = 68
he has 68 apples and 95 oranges at first
To find the number of oranges Jimmy had at first, we need to use algebra.
Let's assume the number of oranges Jimmy had initially is represented by 'o'.
According to the given information, Jimmy had a total of 163 fruits, which is the sum of apples and oranges.
So, we can write an equation: o + a = 163
Now, we know that Jimmy sold 50% of all the apples, which means he had (100% - 50%) = 50% of the original number of apples remaining. Similarly, he sold 20% of all the oranges, so he had (100% - 20%) = 80% of the original number of oranges remaining.
After selling the fruits, he had 110 fruits left, which can be represented as: (0.8 * o) + (0.5 * a) = 110
From the above two equations, we can solve for 'o'.
Substituting the value of 'a' from the first equation into the second equation gives us:
(0.8 * o) + (0.5 * (163 - o)) = 110
Now, we can simplify and solve this equation to get the value of 'o'.
0.8o + 81.5 - 0.5o = 110
0.3o + 81.5 = 110
0.3o = 110 - 81.5
0.3o = 28.5
Dividing both sides of the equation by 0.3 gives us:
o = 28.5 / 0.3
o = 95
Therefore, Jimmy had 95 oranges initially.